Hybrid search runs keyword and semantic retrieval in parallel and merges the two result lists into one ranking. It works because the two methods fail in opposite directions — keyword misses paraphrase, semantic misses identifiers — so their union misses far less than either alone.
The standard technique is reciprocal rank fusion: each result is scored by its position in each list rather than by raw score. This sidesteps the fact that BM25 scores and vector distances are not comparable quantities, and it is robust without tuning.
Weighted score fusion is the alternative, and it needs normalisation plus per-corpus calibration to behave.
Retrieve broadly with both methods, fuse into a candidate set of perhaps fifty, then re-rank that set with a more expensive cross-encoder and apply business rules — availability, margin, merchandising — at the final stage.
This shape is now close to universal in serious search systems, because it puts cheap operations where breadth is needed and expensive ones where precision is needed.
Two indexes to maintain, embedding generation on write, and a re-ranking step on read. For most sites the added latency is tens of milliseconds and the recall improvement is large enough that the trade is not close.